Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
460 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #24907265 | C2 | semidirect |
| 4. #24905591 | C2 | semidirect |
| 6. C2×#14581799 | C4 | semidirect |
| 10. #19127725 | C4 | semidirect |
| 12. #19127668 | C4 | semidirect |
| 15. C2×C4×C83⋊C8 | C4 | semidirect |
| 16. #19127500 | C4 | semidirect |
| 17. #19127498 | C4 | semidirect |
| 157. C83 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916175 | 2 |
| #24909148 | 2 |
| #24907265 | 2 |
| #24905591 | 2 |
| C83×#2126 | 2 |
| #12633 | 83 |